The probability approach to uncertainty and modeling is applied to default probability estimation. This issue has attracted attention as banks contemplate the requirements of Basel IIjs IRB rules. Nicholas M. Kiefer proposes the fomal introduction of expert information into quantitative analysis. An application treating the incorporation of expert information on the default probability is considered in detail.
Estimation of default probabilities (PD), loss given default (LGD, a fraction) and exposure at default (EAD) for portfolio segments containing reasonably homogeneous assets is essential to prudent risk management as well as for compliance with Basel II rules for banks using the IRB approach to determine capital requirementsBasel Committee on Banking Supervision (2004). Estimation of small probabilities is tricky, and I will focus on estimating PD. This problem has attracted considerable recent attention; see Basel Committee on Banking Supervision (2005), Balthazar (2004), BBA, LIBA, and ISDA (2005),and Pluto and Tasche (2005). This is an application in which data information is scarce while expert information is available. The focus of this paper is on estimation of the default probability for a risk bucket on the basis of historical information and expert knowledge. Section 2 argues for the probability approach to uncertainty measurement. The probability approach to default modeling is uncontroversial, although perhaps the extent of the constraints imposed by the simple independent Bernoulli model are under appreciated. This model is briefly described in Section 3.
In section 4 we argue that exactly the same considerations that lead to the probability approach for defaults should lead to the probability approach to default probabilities. As an example, we consider describing expert information in the form of a Beta distribution on the Bernoulli parameter. The probability approach allows coherent combination of expert and data information through Bayes Rule, taken up in Section 5. Section 6 considers estimators of PD based on the probability approach and compares them with alternatives, including the maximum likelihood estimator (which is also the unbiased estimator) and a recent suggestion based on the upper endpoint of a confidence interval of prespecified coverage.
